ABSTRACT
In N ∼ Z nuclei where protons and neutrons occupy the same valence shells, the sdIBM-ST discussed in Chapters 8 and 9 with isoscalar, in addition to isovector, bosons is crucial for odd-odd nuclei. However, for even-even nuclei T = 1 (with S = 0) bosons appear to be adequate. The IBM with protonneutron T = 1 pairs (δ bosons having T = 1 and MT = 0) in addition to the, as in pnIBM for heavy nuclei, proton pairs (π bosons having MT = −1) and neutron pairs (ν bosons having MT = +1) is called IBM-3. As (π, ν, δ) bosons form the isospin triplet of T = 1 bosons, it is possible to consider isospin invariant Hamiltonians and the resulting model with s and d bosons is called sdIBM-T to denote that the s and d bosons of IBM carry isospin T = 1 degree of freedom and the Hamiltonian is T invariant. The sdIBM-T was first proposed by Elliott and White [291]. In the literature, sdIBM-T is often called IBM-3. It should be stressed that sdIBM-T is specific to even-even N ∼ Z nuclei (it will also describe the isobaric analog states in the neighboring odd-odd nuclei). The sdIBM-T has rich algebraic structure and we will focus on this aspect in this chapter. At the end we will discuss briefly the microscopic justification of this model as investigated by Elliott.
